The England captain scored two goals – including an injury-time winner – to secure three points for Gareth Southgate’s side in Volgograd after Ferjani Sassi’s controversial first-half penalty had made it 1-1 ten minutes before half-time.
Kyle Walker was penalised for an elbow on Fakhreddine Ben Youssef, but Kane was denied two strong penalty claims when he was wrestled to the ground at corners by Sassi in the first half and Yassine Meriah after the break, which weren’t awarded despite the availability of VAR.
Kane called on Colombian referee Wilmar Roldan to do better in his next match.
“I was maybe a bit disappointed by that,” the Tottenham striker said after the game.
“You look at the penalty they got. I’ve not seen it back, but on the pitch it looked quite soft.
“I guess that’s what VAR is there for, to look at them decisions. If they don’t think that was a penalty, we have to deal with that.
“For me, I struggled to get them off me. I tried to run at a few corners and couldn’t move. I guess, as players there’s nothing we can do about that.
“We just have to hope the officials get it right more often than not.”
He added: “It’s part of the game. We knew from watching the other games, there’s been a lot of penalties and a lot of soft decisions. We had to be aware of that.
“We had one against us today and probably another couple that didn’t go our way. It’s difficult, but as players all we can do is get on with the game.
“It’s down to the officials and hopefully when they watch it back they will make it right for the next games.”
Rough treatment from Tunisia’s players was not the only issue Kane and his team-mates had to deal with as a plague of midges descended on the Volgograd Arena on Monday.
The England skipper revealed all of the players used repellent before the match and at half-time to deal with the nuisance insects.
He said: “We got told before there were going to be quite a lot of flies and when we went out for the warm-up there was a lot more than we thought.
“We all had a lot of bug spray on before the game and at half-time. That was important because some of them were in your eyes and in your mouth.
“I guess that’s just part of dealing with whatever comes your way. The team coped with it well.”
Kane added that he and his team-mates were pleased with their performance, particularly in the first half.
“It felt good out there,” he said.
“That’s exactly how we wanted to start the game. We attacked the team and created chances. We could have scored two or three goals and put the game to bed early.
“In a World Cup against any team they are always going to fight and keep going and we had to deal with that. We were really pleased with how we played.”